On boundedness and compactness of Riemann-Liouville fractional operators

Let α ∈ (0, 1). Consider the Riemann-Liouville fractional operator of the form with locally integrable weight functions u and v. We find criteria for the Lp → Lq-boundedness and compactness of Tα when 0 < p,q < ∞, p > 1/α under the condition that u monotonely decreases on ℝ+:= [0,∞). The dual versions of this result are given. © 2013 Pleiades Publishing, Ltd.